Swelling Pressure and Retaining Wall Design in

Expansive Soils

A thesis submitted in fulfilment of the requirements for the degree of

Master of Engineering

YA TAN

Bachelor of Engineering (Civil and Infrastructure) at RMIT University

School of Engineering

College of Science Engineering and Health

December 2016

2

Declaration

I certify that except where due acknowledgement has been made, the work is that of the

author alone; the work has not been submitted previously, in whole or in part, to qualify for

any other academic award; the content of the thesis is the result of work which has been

carried out since the official commencement date of the approved research program; any

editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics

procedures and guidelines have been followed.

Ya Tan

December 2016

i

Abstract

A retaining wall constructed on expansive soil can be subjected to lateral swelling

pressures due to soil swelling, which may cause a significant horizontal deformation

and bending of the retaining wall. In Australia, it is generally assumed that the backfill

behind a retaining wall is non-expansive material. Therefore lateral swelling pressures

induced by expansive soils are ignored in routine design. However in cases where

expansive soils are present behind a retaining wall, swelling pressure should be

evaluated based on soil properties and/or laboratory tests so that the wall can be

designed properly to withstand these swelling pressures, which can be significant.

In this study, a retaining wall model, 1 m × 1.415 m × 1 m, was set up for the

laboratory experiment. Expansive soils were filled into the box in 5 layers to achieve the

required soil density. Six load cells were installed on the back of the retaining walls to

measure the lateral pressures developed along the depth of the wall. A laser level was

placed on a top concrete block to measure any vertical movement of soil. Two LVDT

devices placed at the rear of the retaining wall were used to monitor the lateral

movement of the retaining wall. Soil suction changes were monitored using

psychrometer and the filter paper method. Two laboratory experiments were conducted

to evaluate how swelling pressures were developed behind a retaining wall backfilled

with expansive soils with different densities. Each test was run for 80 days.

A series of oedometer tests were also carried out to measure swelling pressures

developed within soil samples with different initial suctions and densities. The results of

oedometer swelling tests indicate that swelling pressures increase with the initial suction

and dry densities. In addition to retaining wall model tests and oedometer tests, a series

of other laboratory tests were performed which include shear box test, shrink-swell test,

soil-water characteristic curve, liquid limit, plastic limit, linear shrinkage, soil suction

measurement, and X-ray diffraction (XRD) test. Based on the laboratory tests, a new

method/equation is developed for the prediction of the lateral swelling pressure of

unsaturated expansive soils behind of retaining walls.

ii

Acknowledgement

Foremost, I am truly indebted to my supervisor Dr. Jie Li, Thanks for his valuable

supervision, critical suggestion, and immense help during my studies, especially in

those periods when I doubted successful completion of my degree. I would also like to

express my deep gratitude to my associate supervisor Dr. Annan Zhou, thanks for his

guidance, continuous helps and patience. Without their persistent encouragement, this

dissertation would not have been possible.

I gratefully acknowledge the assistance of the technical staff at RMIT University,

Haman Tokhi, Kevin Le, Bao Nguyen and Kee Kong Wong and my fellow postgraduate

students, Lei Guo, and Mr. Jian Zou. I would not be able to successfully conduct any

laboratory test without their helps; their useful discussion and supports are invaluable.

Last but not least, I would thank to my family, thanks for my parents’ financial support

during my studies in Australia, thanks to my wife Jiaying for her accompany and

encourages me whole my study time at RMIT University. I am extremely grateful to the

unconditional love, and support from my parents, my wife, my auntie Wei Yan, and my

grandma. To my mother who had sacrificed her happiness to help me overcome my

tough time, your love was an invaluable treasure in my life.

To the memory of my beloved mother, forever loved, missed and remembered.

i

Notation

effective stress

vertical stress

pore air pressure

pore water pressure

net stress

suction

the mass of container

the mass of container and wet soil

the mass of container and dry soil

saturated water content

predicted values of swelling potential

the longitudinal shrinkage of the specimen

shrink swell index

swelling percentage

shrinkage percentage

dry density

lateral earth pressure coefficient at rest

active lateral earth pressure coefficient

pasive lateral earth pressure coefficient

Rankine or Coulomb active force (kN/m)

the angle of inclination of ground surface above the horizontal

'

'v

a

w

s

am

bm

cm

s

pS

sL

ssI

sw

sh

d

0K

aK

pK

aP

ii

back face inclination of the structure

Coulomb theory friction angle

Rankine theory soil fiction angle

shear stress along failure plane

cohesion (kPa)

C clay content

D minimum horizontal distance

volumetric water content

total suction

osmotic suction

degree of saturation

plastic index

volumetric strain

volumetric strain in elastic region

the time taken to reach failure, in minutes

the time taken to reach 50% consolidation, in minutes

logarithmic hardening constant

void ratio

initial void ratio

final void ratio

initial water content

soil sample ring height

f

'c

s

rS

PI

v

e

v

ft

50t

e

0e

fe

iw

h

iii

Table of Contents

Abstract .............................................................................................................................. i

Acknowledgement ............................................................................................................ ii

Notation ............................................................................................................................. i

Table of Contents ............................................................................................................ iii

List of Figures ................................................................................................................... v

List of Tables ................................................................................................................. viii

Chapter 1 Introduction ...................................................................................................... 1

1.1 General .................................................................................................................... 1

1.2 Research Objectives ................................................................................................ 3

1.3 Thesis Arrangement ................................................................................................ 3

Chapter 2 Literature Review............................................................................................. 5

2.1 Introduction ............................................................................................................. 5

2.2 Swelling Potential Expansive soil and Classification Methods .............................. 5

2.2.1 Indirect Measurement Method ......................................................................... 6

2.2.2 Direct Measurement Methods .......................................................................... 9

2.3 Suction in Expansive Soils ................................................................................... 11

2.4 Retaining Wall Design .......................................................................................... 13

2.4.1 Introduction .................................................................................................... 13

2.4.2 Lateral Earth Pressure for Retaining Walls .................................................... 14

2.4.3 Coulomb Theory ............................................................................................ 16

2.4.4 Rankine Theory .............................................................................................. 20

2.4.5 Retaining Wall Design ................................................................................... 22

2.4.6 Stability of rigid retaining walls ..................................................................... 26

Chapter 3 Laboratory Testing ......................................................................................... 30

3.1 Introduction ........................................................................................................... 30

3.2 Atterberg Limit Test ............................................................................................. 31

3.2.1 Plastic Limit Test ........................................................................................... 32

3.2.2 Liquid Limit Test ........................................................................................... 33

3.2.3 Linear Shrinkage Test .................................................................................... 34

3.3 X-ray Diffraction .................................................................................................. 37

iv

3.4 The Shrink Swell Test ........................................................................................... 39

3.4.1 Test Procedure ................................................................................................ 39

3.4.2 The Results of shrink swell testing ................................................................ 43

3.5 Shear Box Tests .................................................................................................... 44

3.6 Soil-Water Characteristic Curve ........................................................................... 48

3.6.1 Testing Procedure ........................................................................................... 51

3.6.2 Test Result ...................................................................................................... 51

3.7 Oedometer Test ..................................................................................................... 54

3.7.1 Test Procedure ................................................................................................ 54

3.7.2 Results of Oedometer Tests............................................................................ 55

3.8 Summary ............................................................................................................... 58

Chapter 4 Retaining Wall Experiments .......................................................................... 59

4.1 Introduction ........................................................................................................... 59

4.2 Soil samples and soil suction measurement .......................................................... 60

4.3 Experimental Setup ............................................................................................... 61

4.4 Result of Retaining Wall Experiments ................................................................. 66

4.4.1 The Load Cell Data ........................................................................................ 66

4.4.2 The Displacement Data .................................................................................. 75

4.4.3 Suction Measurement ..................................................................................... 78

4.5 Summary ............................................................................................................... 88

Chapter 5 Development of New Model for Prediction of Lateral Swelling Pressure .... 90

5.1 Introduction ........................................................................................................... 90

5.2 The proposed new model ...................................................................................... 91

5.3 Summary ............................................................................................................... 96

Chapter 6 Conclusions and Recommendations .............................................................. 97

6.1 Conclusions ........................................................................................................... 97

6.2 Recommendations for Further Work .................................................................... 98

References ...................................................................................................................... 99

v

List of Figures

Figure 1.1: Location of expansive soils around the world (Chen 1975) .......................... 1

Figure 1.2: Location of expansive soil in Australia (Cameron, 2015) ............................. 2

Figure 2.1: Stresses on soil elements in front of and behind retaining wall (Budhu 2010)

........................................................................................................................................ 14

Figure 2.2: The Mohr-Coulomb failure envelope (Budhu 2010) ................................... 15

Figure 2.3: Coulomb failure wedge (Budhu 2010)......................................................... 16

Figure 2.4: Retaining wall with sloping back, wall friction, and sloping soil surface for

use with Coulomb’s method for active condition (Budhu 2010) ................................... 18

Figure 2.5: Retaining wall with sloping soil surface, frictionless soil-wall interface, and

sloping back for use with Rankine’s method (Budhu 2010) .......................................... 20

Figure 2.6: Types of rigid retaining walls (Budhu 2010) ............................................... 22

Figure 2.7: Types of flexible retaining walls (Budhu 2010) .......................................... 23

Figure 2.8: The failure modes of rigid retaining wall (Budhu 2010) ............................. 25

Figure 2.9: The failure modes of flexible retaining wall (Budhu 2010) ........................ 26

Figure 2.10: Forces on rigid retaining walls ................................................................... 27

Figure 3.1: Soil sample preparation ................................................................................ 31

Figure 3.2: Plastic limit test ............................................................................................ 32

Figure 3.3: Liquid limit test ............................................................................................ 33

Figure 3.4: Linear shrinkage test .................................................................................... 35

Figure 3.5: Plasticity chart showing soil studied ............................................................ 36

Figure 3.6: X-ray Diffraction of Glenroy Soil ................................................................ 37

Figure 3.7: X-ray Diffraction of Braybrook Soil ............................................................ 38

Figure 3.8: Core shrinkage test ....................................................................................... 40

Figure 3.9: Apparatus used for the swelling test ............................................................ 41

Figure 3.10: Apparatus used for the direct shear testing ................................................ 44

Figure 3.11: Shear strength vs normal stress (dry density = 14 kN/m3) ......................... 45

Figure 3.12: Shear strength vs normal stress (dry density = 17.4 kN/m3) ...................... 46

Figure 3.13: Shear strength vs normal stress (dry density = 18 kN/m3) ......................... 46

Figure 3.14: Expample of soil-water characteristic curve (Sillers et al. 2001) .............. 48

Figure 3.15: Gravimetric water content versus soil suction for Glenroy soil................. 52

Figure 3.16: Degree of saturation versus soil suction for Glenroy soil .......................... 53

Figure 3.17: Swelling pressure versus initial suction ..................................................... 55

vi

Figure 3.18: Swelling pressure versus initial moisture content ...................................... 56

Figure 3.19: Swelling pressure versus dry density ......................................................... 57

Figure 4.1: Psychrometer calibration with Sodium Chloride solutions ......................... 60

Figure 4.2: Retaining wall arrangement (showing location of load cells)...................... 61

Figure 4.3: Retaining wall set-up – bottom layer ........................................................... 62

Figure 4.4: Retaining wall arrangement (showing location of filter papers).................. 63

Figure 4.5: Retaining wall set up – second layer ............................................................ 64

Figure 4.6: Retaining wall set up – top concrete block, laser and LVDT devices ......... 64

Figure 4.7: Model retaining wall set up for experiments ............................................... 65

Figure 4.8: Measured lateral swelling pressure versus time for load cell 1~3 ............... 67

Figure 4.9: Measured lateral swelling pressure versus time for load cell 4 and 5 .......... 69

Figure 4.10: Measured vertical swelling pressure versus time ....................................... 70

Figure 4.11: Measured lateral swelling pressure versus time for load cells 1, 2 and 3 .. 72

Figure 4.12: Measured swelling pressure versus time for load cell 4 ............................ 73

Figure 4.13: Measured vertical swelling pressure versus time ....................................... 74

Figure 4.14: Displacements of retaining wall versus time (Experiment 1) .................... 76

Figure 4.15: Displacements of retaining wall versus time (Experiment 2) .................... 77

Figure 4.16: Matric suction measured using the contact filter paper method (Experiment

1) ..................................................................................................................................... 80

Figure 4.17: Matric suction measured using the contact filter paper method (Experiment

2) ..................................................................................................................................... 82

Figure 4.18: Total suction of the soil behind the center of the wall measured using WP4

(Experiment 1) ................................................................................................................ 83

Figure 4.19: Total suction of the soil behind the center of the wall measured using WP4

Experiment 2) ................................................................................................................. 84

Figure 4.20: Location of Psychorometer sensors embedded behind of retaining wall

(Experiment 1) ................................................................................................................ 85

Figure 4.21: Soil suction measured using psychrometers (Experiment 1) ..................... 86

Figure 4.22: Location of psychorometer sensors embedded behind of retaining wall

(Experiment 2) ................................................................................................................ 87

Figure 4.23: Soil suction measured using psychrometers (Experiment 2) ..................... 88

Figure 5.1: Multiple regression analysis by Metlab ....................................................... 92

Figure 5.2: Regression equation obtained using Metlab ................................................ 93

vii

Figure 5.3: Effect of initial dry density on the predicted swelling pressure ................... 94

Figure 5.4: Effect of initial moisture content on the predicted swelling pressure .......... 95

Figure 5.5: Effect of shrink-swell index on the predicted swelling pressure, ................ 96

viii

List of Tables

Table 1: Classification of expansive soils (FHA 1973) – from Meehan & Karp (1994) . 6

Table 2: Prediction of soil expansivity by using LL and PI (Chen 1975) ........................ 7

Table 3: Expansive soil classification based on Atterberg limits (Snethen.1984) ........... 7

Table 4: Liquid limit range and site classification (Kay 1990) ........................................ 8

Table 5: Summary of expansive soils classification (Mansour 2011) .............................. 8

Table 6: Values of PVC rating (Lambe 1961) .................................................................. 9

Table 7: Correction factors to be applied to KpC to approximate a logarithm spiral slip

surface for a backfill with a horizontal surface and sloping wall face (Budhu 2010) .... 19

Table 8: Results of liquid limit, plastic limit and linear shrinkage tests ........................ 35

Table 9: Results of Shear Box Testing ........................................................................... 47

1

Chapter 1

Introduction

1.1 General

Expansive soil (also referred to as swelling soil or reactive soil) has long been

recognized as important problem soil in geotechnical engineering. Expansive soil is a

clay soil that has a tendency to expand as its water content increases, and shrink when it

dries out. This volume changes can cause damage to lightweight structures such as

residential building, retaining walls, road and pavement (Li and Cameron, 2002；

Delaney et al. 2005). Damage to lightly loaded structures founded on expansive soils

has been widely reported throughout the world (Li et al. 2014). The problem is

particularly significant in Australia as approximately 20% of the surface area in

Australia is covered by expansive soils (Li and Zhou, 2013; Cameron, 2015). A map of

the distribution of expansive soils around world and in Australia is provided in Figures

1.1 and 1.2 respectively.

Figure 1.1: Location of expansive soils around the world (Chen 1975)

2

Figure 1.2: Location of expansive soil in Australia (Cameron, 2015)

A retaining walls constructed on expansive soil may be subjected to lateral swelling

pressures and friction forces due to the swelling of the soils, which may cause a large

horizontal deformation and bending of the retaining wall. In Australia, it is generally

assumed that the backfill behind a retaining wall is non-expansive material. Therefore

lateral swelling pressures induced by expansive soils are ignored in conventional design.

However, field evidences indicated that horizontal swelling pressures and strains can

affect the performance of structures. For example, Chen (1988) found that in the highly

expansive soil area of South Denver, USA, a number of residential houses had bowing

basement walls with horizontal deflection as much as six inches (15.2 cm) due to the

lateral swelling pressures. Therefore both theoretical and experimental research is

needed to improve the current design methods.

3

In cases where expansive soils are present behind a retaining wall, swelling pressures

should be evaluated based on soil properties and laboratory tests so that the wall can be

designed properly to withstand these swelling pressures, which can be significant.

1.2 Research Objectives

The main objective of this research study is to develop a model/method which can be

used by the local geotechnical engineers to predict swelling pressure acting on the

retaining wall.

The specific objective of this research study includes:

To investigate the properties of expansive soil, by conducting relevant laboratory

experiments including Atterberg limit test, shear box test, shrink-swell test, soil-

water characteristic curve test, and X-ray diffraction.

To measure the swelling pressures developed within soil samples with different

initial moisture contents and densities.

To evaluate the relationship between the index properties and swelling pressure of

expansive soils.

To simulate a retaining wall against lateral swelling pressure caused by expansive

soil in the laboratory.

1.3 Thesis Arrangement

This thesis is divided into 6 chapters. A brief description of each chapter is given below.

Chapter 1 – Introduction

This chapter provides an introduction and the main objectives of the research with

background information on expansive soils and routine design of retaining wall. Thesis

arrangement is outlined in this chapter as well.

4

Chapter 2 – Literature Review

This chapter provides an elaborative review on properties of expansive soil. There are

two major methods for estimating the swelling potential of expansive soil, i.e. direct

measurements and indirect measurements. The direct measurements include oedometer

swelling test and constant volume swell test. The indirect measurement methods such as

index property method, PVC method and activity method use the plasticity index and

liquid limit to estimate the swelling potential of expansive soils. The traditional

retaining wall design methods are introduced in this chapter as well.

Chapter 3 – Laboratory Testing

In this chapter, the laboratory testing is discussed in details, which includes set-up and

preparation of experiments, soil used for testing, and the test procedures. The results of

tests are presented and discussed as well.

Chapter 4 – Retaining Wall Experiments

In this study a model retaining wall was built at RMIT geotechnical laboratory to

simulate the retaining wall against lateral swelling pressure developed within soil.

Chapter 4 describes the experimental set-up and procedure. The experimental results are

also presented and discussed in Chapter4.

Chapter 5 – Development of New Model for Prediction of Lateral Swelling Pressure

In this chapter, a new model is proposed to estimate/predict the lateral swelling

pressures behind a retaining wall, which is based on shrinkage-swell index, initial

moisture content and the dry density.

Chapter 6 – Conclusions and Recommendations

This chapter provides the final conclusions and recommendations for future research.

5

Chapter 2

Literature Review

2.1 Introduction

Expansive soil has attracted the attention of many researchers and practitioners all over

the world, studying the behaviors of expansive soil and its damage to infrastructure such

as buildings, road, pavements and earth retaining structures. Many factors have an effect

on the behaviors of expansive soil, including moisture content (soil suction), dry density,

liquid limit and plasticity index and swelling potential. In this chapter, classification

methods of expansive soils and current retaining wall design methods are outlined.

2.2 Swelling Potential Expansive soil and Classification Methods

Expansive soil has been of great concern to design and geotechnical engineers for many

years. In fact, the first research ever that attempted to study the behaviors of expansive

soil was to prevent damages cause by expansive soil to earth retaining structure of

infrastructure which was presented in the First International Conference on Soil

Mechanics and Foundation Engineering (ISSMGE) held in June 1936 at Harvard

University.

Prediction of swelling potential and swelling pressure has been a problem to civil

engineering for a long time. Swelling potential of expansive soil depends on a number

of factors such as the type and amount of clay minerals, soil structures (i.e. particle

arrangement, bonding, and fissures) and nature of pore fluid, and exchangeable cations

(Mansour 2011).

A number of different methods have been proposed for prediction of swelling potential

and swelling pressure (Chen 1975). Generally, there are two major methods for

estimating the swelling potential of expansive soil:

6

1) Indirect measurement method in which one or more of the related intrinsic

properties of expansive soils are measured and complemented with experience to

estimate swelling potential.

2) Direct measurement method which involves actual measurement of volume

change of expansive soil.

2.2.1 Indirect Measurement Method

There are several indirect measurement methods which are commonly used to estimate

the swelling potential of expansive soils, such as index property method, PVC method

and activity method. These methods are discussed in the following sections.

2.2.1.1 Index Property Method based Atterberg Limits Test

Atterberg limit test is the most common test to determine basic soil properties (i.e.

liquid limit, plastic limit and plasticity index) in current engineering practice. Plasticity

index (PI) and liquid limit (LL) have been used to classify reactivity or expansiveness of

expansive soils by the Federal Housing Administration (Meehan and Karp 1994) since

early 1970s. According to Table 1, soils can be classified into five classes/groups based

on their PI and LL.

Table 1: Classification of expansive soils (FHA 1973) – from Meehan & Karp (1994)

Classification Plasticity index Liquid limit Soil Group

Non-expansive soil 0-6 0-25 A

Marginal 6-10 25-30 B

Moderately expansive 10-25 30-50 C

Highly expansive >25 >50 D

Expansive claystone >50 >70 E

7

Chen (1975) also proposed to adopt PI and LL as indicators to describe the swelling

potential of expansive soils (see Table 2). Based on Table 2, the soil is essentially non-

expansive when the liquid limit is less than 20 percent and the plasticity index is less

than 6 percent.

Table 2: Prediction of soil expansivity by using LL and PI (Chen 1975)

Degree of expansion Liquid limit Plasticity index

Low <30 0-15

Medium 30-40 10-35

High 40-60 20-55

Very High >60 >35

Snethen (1984) evaluated a number of published criteria for classifying swelling

potential and found that liquid limit and plasticity index are best indicators of swelling

potential and soil suction at natural moisture content can be used as decent indicators of

potential swell if natural conditions are taken into account as well. A statistical analysis

of a large amount of testing data resulted in the classification system as shown in Table

3. The US Department of the Army (1983) and the American Association of State

Highway and Transportation Officials (AASHTO, 2008) both adopted the criteria

(Table 3) proposed by Snethen (1984).

Table 3: Expansive soil classification based on Atterberg limits (Snethen.1984)

Potential swell

classification

Liquid

limit (%)

Plasticity

index (%)

Natural soil

suction (tsf)

Potential swell

(%)

High >60 >35 >4 >1.5

Marginal 50-60 25-35 1.5-4 0.5-1.5

Low <50 <25 <1.5 <0.5

8

Table 4 was proposed by Kay (1990). He suggested that the liquid limit is a decent

indicator of shrink-swell response for natural soil although the test was conducted on

reconstituted soil.

Table 4: Liquid limit range and site classification (Kay 1990)

Site Classification Liquid limit range

S (slightly expansive) <20

M (moderately expansive) 20-40

H (highly expansive) 40-70

E (extremely expansive) >70

Based on the above tables, Mansour (2011) proposed to use the following table for

classification of expansive soils

Table 5: Summary of expansive soils classification (Mansour 2011)

Classification Plasticity index (%) Liquid limit (%)

Non-expansive 0-6 0-25

Low <25 25-50

Marginal 25-35 50-60

High >35 >60

2.2.1.2 Potential Volume Change Method (PVC)

The potential volume change (PVC) method was developed by Labme (1961) which has

been extensively used by the Federal Housing Administration as well as many US State

Highway Departments. The PVC test consists of placing a remolded soil sample into an

oedometer ring, wetting it and allowing the sample to swell against a proving ring. The

swell index is essentially a measurement of the swelling pressure exerted by the soil

sample and is correlated to qualitative range of potential volume change using a chart

given by Lambe (1961).

9

Table 6 shows the swelling categories based on the PVC method (Lambe 1961). It

should be pointed out that the PVC values should only be used for comparison of

various swelling soils and not be used as design parameters since the test uses remolded

samples.

Table 6: Values of PVC rating (Lambe 1961)

Category PVC Rating

Very critical >6

Critical 4-6

Marginal 2-4

Non-critical <2

2.2.1.3 Activity Method

The activity method was proposed by Seed et al (1962). This method was based on

remolded artificially prepared soils. The activity is defined as

(2.1)

Where

𝑃𝐼 = 𝑃𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝑖𝑛𝑑𝑒𝑥 (%);

𝐶 = 𝑡ℎ𝑒 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐𝑙𝑎𝑦 𝑠𝑖𝑧𝑒 𝑓𝑖𝑛𝑒𝑟 𝑡ℎ𝑎𝑛 0.002𝑚𝑚.

2.2.2 Direct Measurement Methods

The direct methods involve actual measurement of the swell parameters of expansive

soil. Therefore they are more reliable than the indirect methods. The disadvantage of the

direct methods is that they usually require special equipment and time consuming (i.e.

not suitable for quick identification of expansive soils).

C-10

PIActivity

10

There are three types of oedometer tests which are used to evaluate the swelling

characteristics: (1) constant volume swell test, (2) improved swell oedometer test and (3)

swell overburden test. These tests are outlined in ASTM D4546 (2003) accept the

shrink-swell test which is introduced in Australian Standard AS 1289.7.1 (2003).

2.2.2.1 Constant Volume Swell Test

In this technique, soil specimen is placed into the oedometer cell and its vertical

expansion when inundated with water is prevented by progressively loading the

specimen. Once no more expansion is observed when saturation is completed, the final

total pressure applied to the specimen represents a direct measure of swelling pressure.

2.2.2.2 Improved Swell Oedometer Test

In the improved oedometer test, the sample is allowed to swell freely in the vertical

direction under a seating load of 7 kPa until the primary swell is completed. The sample

is then loaded to its initial height. The pressure that brings the sample to its initial height

(i.e. zero swell) can be taken as the swelling pressure.

2.2.2.3 Swell Overburden Test

In the swell overburden test, the specimen is loaded to in situ overburden pressure or a

predetermined surcharge pressure, inundated with water under this pressure until the

primary swell is completed. The specimen is then loaded until it reaches to its original

height (i.e. at 0% vertical swell).

11

2.2.2.4 Shrinkage-Swell Test

In Australia, methods for directly testing the swelling potential of expansive soils are

given in AS1289.7.1.1 (2003). The shrink-swell test consists of a core shrinkage test

and a swelling test. During the core shrinkage test, a cylindrical core sample is allowed

to dry out in air on a smooth surface for a period of approximately 1-2 weeks. Two

drawing pins are placed in the centre of the core at either end and the distance between

the rounded heads of the pins is regularly measured with a digit vernier calliper to the

nearest 0.01 mm. The core shrinkage test is used to obtain the shrinkage strain. In the

swelling test, the specimen is placed into a consolidation cell which is inundated with

water and allowed to swell under a vertical pressure equal to the overburden pressure or

25 kPa. The swelling displacement is regularly recorded.

After obtaining the shrinkage strain and swelling strain, the shrink-swell index of a soil

can be calculated by the following equation (AS1289.7.1.1, 2003):

𝐼𝑠𝑠 =

휀𝑠𝑤2⁄ + 휀𝑠ℎ

1.8

(2.3)

Where

𝐼𝑠𝑠 = 𝑠ℎ𝑖𝑛𝑘𝑎𝑔𝑒 − 𝑠𝑤𝑒𝑙𝑙 𝑖𝑛𝑑𝑒𝑥;

휀𝑠𝑤 = 𝑠𝑤𝑒𝑙𝑙𝑖𝑛𝑔 𝑠𝑡𝑟𝑎𝑖𝑛;

휀𝑠ℎ = 𝑠ℎ𝑖𝑛𝑘𝑎𝑔𝑒 𝑠𝑡𝑟𝑎𝑖𝑛.

2.3 Suction in Expansive Soils

A retaining wall constructed on expansive soil is subjected to the lateral swelling

pressure due to soil swelling caused by a change in soil suction. Soil suction is an

important parameter in describing the moisture stress condition of unsaturated soils. Soil

suction, usually expressed in pF or kPa, is a measure of a soil’s affinity for moisture.

12

Therefore, “dry” soils which have a higher affinity to absorb moisture have high values

of kPa (pF), while “wet” soils which have a low affinity to absorb more moisture have

low values of kPa (pF).

The total suction is equal to the sum of osmotic (or solute) suction and matric suction.

Osmotic suction is a measure of the potential to build water in the soil due to the

osmotic effects of the solutes in the bulk soil solution. This type of suction refers to the

potential of the soil and water to bind due to osmotic effects of the solutes in the bulk

soil solution. Matric suction refers to the soil’s affinity for water at the same salinity

level (AS2870, 2011) and relies upon capillary forces generated by the small radius of

the interface between water and air within the voids in the soil.

Soil suction can be measured both directly and indirectly. Direct methods used to

measure matrix suction include tensiometer, pressure plate, pressure membrane, and

psychrometers technique. Indirect matric suction measurements include filter paper

technique, electrical conductivity sensors, time domain reflectometry (TDR) and

thermal conductivity sensor. Osmotic suction can be measured indirectly using several

methods, such as saturation extract method and pore fluid squeezer technique.

13

2.4 Retaining Wall Design

2.4.1 Introduction

Retaining walls have been widely used in civil engineering and construction for

stabilizing slopes and excavations. Estimating lateral earth pressures has been of

geotechnical interest for well over a century because a safe retaining wall design

requires accurate prediction of earth pressure imposed on the retaining wall by soils.

There are two methods for calculation of lateral earth pressures which are widely used

in routine design. One was developed by Coulomb (1776) and the other by Rankine

(1856). These two methods differ in the assumptions made to simplify the problem, but

both are very simple in application. Coulomb’s method for the determination of lateral

earth pressure was based on the limit equilibrium, which includes wall friction, wall

slope, and backfill slope. Rankine’s method was based on the stress states of the backfill

materials which do not consider wall friction. The failure plane assumed by both

Coulomb and Rankine methods is planner surface.

There are various types of retaining walls. Retaining walls can be broadly classified into

three categories: mass gravity, flexible or sheet pile and mechanically stabilized earth

walls. The gravity retaining wall is a massive concrete wall relying on its mass to resist

the lateral force from the retain soil mass. Flexible or sheet pile wall is long, slender

wall relying on passive resistance and anchors or props for its stability. Mechanically

stabilized earth is a gravity-type retaining wall in which the soil is reinforced by thin

reinforcing elements. (Budhu 2010)

14

2.4.2 Lateral Earth Pressure for Retaining Walls

The lateral earth pressures on a vertical wall that retains a soil mass dealt with two

theories that are Coulomb’s earth pressure theory and Rankine’s earth pressure theory.

The pressures on the retaining walls cause movements and its three different lateral

earth pressures conditions are shown in Figure 2.1 (Budhu 2010).

Figure 2.1: Stresses on soil elements in front of and behind retaining wall (Budhu

2010)

If the wall remains the rigid and no movement, then the effective stresses at rest on

element A and element B are:

𝜎𝑧′ = 𝜎1

′ = 𝛾′𝑧 (2.1)

𝜎𝑥′ = 𝜎3

′ = 𝐾0𝜎1′ = 𝐾0𝛾′𝑧 (2.2)

Where

γ' is the effective unit weight of soil;

K0 is the lateral earth pressure at rest.

15

Figure 2.2: The Mohr-Coulomb failure envelope (Budhu 2010)

Based on Figure 2.2, the Ka and Kp is given:

𝐾𝑎 = tan2(45 −𝜙′

2)

(2.3)

𝐾𝑝 = tan2(45 +𝜙′

2)

(2.4)

Where

Ka is active lateral earth pressure coefficient;

Kp is passive lateral earth pressure coefficient.

Therefore Ka = 1/Kp.

16

2.4.3 Coulomb Theory

Coulomb’s analysis of lateral earth forces on a retaining structure is based on limit

equilibrium. And a soil mass behind a vertical retaining wall will slip along a plane

inclined an angle θ to the horizontal as Figure 2.3. Then the slip plane was determined

by the maximum thrust acts on the plane. The basic tenets of the model consist of:

(1) selection of a plausible failure mechanism,

(2) determination of the forces acting on the failure surface, and

(3) use of equilibrium equations to determine the maximum thrust.

Figure 2.3: Coulomb failure wedge (Budhu 2010)

∑ 𝐹𝑥 = 𝑃 + 𝑇 cos 𝜃 − 𝑁 sin 𝜃 = 0 (2.5)

∑ 𝐹𝑧 = 𝑊 − 𝑇 sin 𝜃 + 𝑁 cos 𝜃 = 0 (2.6)

The weight of sliding mass of soil is

W =1

2𝛾𝐻0

2 cot 𝜃 (2.7)

At limit equilibrium,

T = N tan 𝜙′ (2.8)

17

Solving for P

P =1

2𝛾𝐻0

2 cot 𝜃 tan(𝜃 − 𝜙′) (2.9)

The maximum thrust and the inclination of the slip line was determined by using

calculus to differentiate Equation 2.9 with respect to θ.

𝜕𝑃

𝜕𝜃=

1

2𝛾𝐻0

2 [cot 𝜃 𝑠𝑒𝑐2(𝜃 − 𝜙′) − 𝑐𝑠𝑐2θtan(𝜃 − 𝜙′)] = 0 (2.10)

Which leads to

θ = 𝜃𝑐𝑟 = 45 +𝜙′

2

(2.11)

Substituting θ into Equation 2.9,

P = 𝑃𝑎 =1

2𝛾𝐻0

2𝑡𝑎𝑛2 (45𝑜 −𝜙′

2) =

1

2𝐾𝑎𝛾𝐻0

2 (2.12)

From the Figure 2.4, the retaining structure has wall friction (δ), the wall face

inclination of vertical with an angle η and back fill is sloping at an angle β. Based on

Coulomb limit equilibrium approach, Poncelet (1840) obtained expressions for Ka and

Kp and the lateral earth pressure coefficients was estimated below:

𝐾𝑎𝐶 =cos2(𝜙′ − 𝜂)

cos2 𝜂cos(𝜂 + 𝛿)[1 + {sin(𝜙′ + 𝛿) sin(𝜙′ − 𝛽)cos(𝜂 + 𝛿) cos( 𝜂 − 𝛽)

}1

2⁄ ]2

(2.13)

𝐾𝑝𝐶 =cos2(𝜙′ + 𝜂)

cos2 𝜂cos(𝜂 − 𝛿)[1 − {sin(𝜙′ + 𝛿) sin(𝜙′ + 𝛽)cos(𝜂 − 𝛿) cos( 𝜂 − 𝛽)

}1

2⁄ ]2

(2.14)

Where KpC ≠ 1/KaC and lateral earth pressure coefficients are applied to the principal

effective stress.

𝐾𝑎𝐶 = 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑒𝑎𝑟𝑡ℎ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑎𝑐𝑡𝑖𝑣𝑒 𝑠𝑡𝑎𝑡𝑒

𝐾𝑝𝐶 = 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑒𝑎𝑟𝑡ℎ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑝𝑎𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑎𝑡𝑒

𝜙′ = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛;

𝛿 = 𝑤𝑎𝑙𝑙 𝑓𝑖𝑟𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒;

18

𝜂 = 𝑠𝑙𝑜𝑝𝑒 𝑖𝑛𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛;

𝛽 = 𝑏𝑎𝑐𝑘 𝑓𝑎𝑐𝑒 𝑖𝑛𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒.

Figure 2.4: Retaining wall with sloping back, wall friction, and sloping soil surface

for use with Coulomb’s method for active condition (Budhu 2010)

The inclination of the slip plane to the horizontal for a horizontal backfill is

tan 𝜃 = [(sin 𝜙′ cos 𝛿)1/2

cos 𝜙′{sin(𝜙′ + 𝛿)}1/2] ± tan 𝜙′

(2.15)

Where the positive sign is refer to the active state (θ = θa) and the negative sign refer to

the passive state (θ = θP).

Both of the active state and passive state has curved slip planes caused by wall friction

and the curvature of active state is smaller than passive state. The curved slip surface

leaded inaccurate value of KaC and KpC. However the error for the active state is small

and can be neglect, and an overestimation of the passive state using Coulomb’s analysis.

So many investigators attempted to find more accurate Kp using different methods such

that Caquot and Kerisel (1948) used logarithm spiral slip surface method and Packshaw

19

(1969) used circular failure surface method. Table 7 showed below lists factors that Kpc

can be used to correct it for logarithm spiral slip surface.

Table 7: Correction factors to be applied to KpC to approximate a logarithm spiral

slip surface for a backfill with a horizontal surface and sloping wall face (Budhu

2010)

δ/Φ’

Φ’ -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

15 0.96 0.93 0.91 0.88 0.85 0.83 0.8 0.78

20 0.94 0.9 0.86 0.82 0.79 0.75 0.72 0.68

25 0.91 0.86 0.81 0.76 0.71 0.67 0.62 0.57

30 0.88 0.81 0.75 0.69 0.63 0.57 0.52 0.47

35 0.84 0.75 0.67 0.6 0.54 0.48 0.42 0.36

40 0.78 0.68 0.59 0.51 0.44 0.38 0.32 0.26

The later force is inclined at an angle δ from the normal to the wall face. The direction

of the friction force depended on whether the wall moves relative to the soil or the soil

moves relative to the wall. As can be seen from Figure 2.4, that the active wedge moves

downward relative to the wall and the passive wedge moves upward relative to the wall.

The active lateral force has the positive sense of the inclination and the passive lateral

force negative sense of the inclination, and the application point of these forces is H0/3

from the base of the wall.

20

2.4.4 Rankine Theory

Rankine earth pressure theory is usually used to determine the lateral earth pressures for

vertical, frictionless wall supporting a dry, homogeneous soil with a horizontal surface.

According to the Rankine theory, the expressions for KaR and KpR are given below with

reference to Figure 2.5

Figure 2.5: Retaining wall with sloping soil surface, frictionless soil-wall interface,

and sloping back for use with Rankine’s method (Budhu 2010)

𝐾𝑎𝑅 =cos( 𝛽 − 𝜂) √1 + sin2 𝜙′ − 2 sin 𝜙′ cos 𝜔𝑎

cos2𝜂(cos 𝛽 + √sin2 𝜙′ − sin2 𝛽)

(2.16)

and

𝐾𝑝𝑅 =cos( 𝛽 − 𝜂) √1 + sin2 𝜙′ + 2 sin 𝜙′ cos 𝜔𝑝

cos2𝜂(cos 𝛽 − √sin2 𝜙′ − sin2 𝛽)

(2.17)

Where

𝐾𝑎𝑅 = 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑒𝑎𝑟𝑡ℎ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑎𝑐𝑡𝑖𝑣𝑒 𝑠𝑡𝑎𝑡𝑒

𝐾𝑝𝑅 = 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑒𝑎𝑟𝑡ℎ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑝𝑎𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑎𝑡𝑒

𝜙′ = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛;

21

𝜉 = 𝑤𝑎𝑙𝑙 𝑓𝑖𝑟𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒;

𝜂 = 𝑠𝑙𝑜𝑝𝑒 𝑖𝑛𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛

𝛽 = 𝑏𝑎𝑐𝑘 𝑓𝑎𝑐𝑒 𝑖𝑛𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒

𝜔𝑎 = sin−1 (sin 𝛽

sin 𝜙′) − 𝛽 + 2𝜂

(2.18)

𝜔𝑝 = sin−1 (sin 𝛽

sin 𝜙′) + 𝛽 − 2𝜂

(2.19)

The angles of the failure planes to the horizontal for active and passive states are:

𝜃𝑎 =𝜋

4+

𝜙′

2+

𝛽

2−

1

2sin−1 (

sin 𝛽

sin 𝜙′)

(2.20)

𝜃𝑝 =𝜋

4−

𝜙′

2+

𝛽

2+

1

2sin−1 (

sin 𝛽

sin 𝜙′)

(2.21)

The sign conventions for η and β are shown in Figure 2.5; counterclockwise rotation is

positive.

The active and passive lateral earth forces at the limiting stress state are:

𝑃𝑎 =1

2𝐾𝑎𝑅𝛾′𝐻0

2 and 𝑃𝑎 =1

2𝐾𝑝𝑅𝛾′𝐻0

2

The inclinations of the normal of the wall face for the forces:

𝜉𝑎 = tan−1(sin 𝜙′ sin 𝜃𝑎

1 − sin 𝜙′ cos 𝜃𝑎)

(2.22)

𝜉𝑝 = tan−1(sin 𝜙′ sin 𝜃𝑝

1 + sin 𝜙′ cos 𝜃𝑝)

(2.23)

In the case of a wall with a vertical face, η = 0,

𝐾𝑎𝑅 =1

𝐾𝑝𝑅= cos 𝛽(

cos 𝛽 − √𝑐𝑜𝑠2𝛽 − 𝑐𝑜𝑠2𝜙′

cos 𝛽 + √𝑐𝑜𝑠2𝛽 − 𝑐𝑜𝑠2𝜙′)

(2.24)

The active and passive lateral earth forces work on a direction parallel to the soil surface,

the inclination of angle β to the horizontal, therefore Pax = Pa cos β and Paz = Pa sin β.

22

2.4.5 Retaining Wall Design

Generally, there are three classes of retaining walls, i.e. cast-in-place (CIP) gravity and

semi-gravity walls, and flexible retaining wall (Budhu 2010). CIP gravity and semi-

gravity walls are rigid and constructed by concrete relying on gravity for stability.

Flexible retaining walls are constructed by long and slender members and rely on

passive soil resistance and anchors for stability (Figure 2.6). The common materials

used of flexible retaining wall consist of steel, concrete, and timber.

Figure 2.6: Types of rigid retaining walls (Budhu 2010)

23

Figure 2.7: Types of flexible retaining walls (Budhu 2010)

According to Das 2007, there are four types of retaining wall as follows:

1. The gravity wall depends mostly on its own weight for stability. It is the oldest and

most frequently used retaining walls. Gravity retaining walls can be built of stone or

concrete. It has the advantage of using local materials, construction convenience, and

good economic results. Therefore, gravity retaining wall has been widely used in

railways, highways, water conservancy, harbor, mining and other projects. As the

gravity retaining wall to maintain balance and stability by its own weight, therefore, the

volume and weight are large; the construction of such heavy wall on the soft foundation

is often limited by the bearing capacity of soil foundation.

2. The structural stability of the cantilever retaining wall is ensured by the weight of the

wall and the gravity of the fill above the heel plate, and the wall toe plate also

24

significantly increases the anti-overturning stability and greatly reduces the stress of the

foundation. Its main advantages are simple structure, convenient construction, smaller

wall section, its light weight, can play a better strength property of materials, can adapt

to lower bearing capacity of the foundation. It is suitable for the lack of stone and

earthquake areas.

3. Counterfort retaining walls are similarities with cantilever wall for construction.

Counterfort retaining walls can restrict more bearing capacity and shear force

comparison with cantilever retaining wall.

4. Sheet piling retaining walls are built in comparatively soft soils such as expensive

soils and tight spaces, which the function is for temporary structures like braced cuts.

Moreover, they have another usage with a varying purpose for excavation support

system and floodwalls also cut-off walls. Cantilever and anchored sheet pile are the two

basic types of sheet pile walls can be used for a wall height larger than 4.5m (Day 1994).

25

There are four modes of failure for a rigid retaining wall: (a) translational failure, (b)

rotation and bearing capacity failure, (c) deep-seated failure, and (d) structural failure.

Figure 2.8: The failure modes of rigid retaining wall (Budhu 2010)

26

The modes of failure for sheet pile walls are shown in as follows:

Figure 2.9: The failure modes of flexible retaining wall (Budhu 2010)

2.4.6 Stability of rigid retaining walls

Translation

A rigid retaining wall must have adequate resistance against translation, which is the

sliding resistance of the base of the wall greater than the lateral force pushing on the

wall. The factor of safety against translation is:

(FS)𝑇 =𝑇

𝑃𝑎𝑥; (FS)𝑇 ≥ 1.5

(2.25)

Where

27

T is the sliding resistance at the base;

Pax is the lateral force pushing on the wall.

T = 𝑅𝑧 tan 𝜙𝑏′ , for an ESA; (2.26)

T = 𝑠𝑤𝐵, for a TSA (2.27)

Where

Rz is the resultant vertical force;

sw is the adhesive stress;

B is the horizontal width of the base;

𝜙𝑏′ is the interfacial friction angle between the base of the wall and the soil.

𝜙𝑏′ ≈

1

2𝜙𝑐𝑠

′ 𝑡𝑜 2

3𝜙𝑐𝑠

′

Typical sets of forces acting on gravity and cantilever rigid retaining walls are showed

in Figure 2.10

Figure 2.10: Forces on rigid retaining walls

For an ESA,

(FS)𝑇 =[(𝑊𝑤 + 𝑊𝑠 + 𝑃𝑎𝑧) cos 𝜃𝑏 − 𝑃𝑎𝑥 sin 𝜃𝑏] tan 𝜙𝑏

′

𝑃𝑎𝑥 cos 𝜃𝑏 + (𝑊𝑤 + 𝑊𝑠 + 𝑃𝑎𝑧) sin 𝜃𝑏

(2.28)

Where

Ww is the weight of the wall,

28

Ws is the weight of the soil wedge,

Paz is the vertical components of the active lateral force,

Pax is the horizontal components of the active lateral force.

θb is the inclination of the base to the horizontal.

If θb is 0 (the base of a retaining wall is horizontal), then:

(FS)𝑇 =[(𝑊𝑤 + 𝑊𝑠 + 𝑃𝑎𝑧) tan 𝜙𝑏

′

𝑃𝑎𝑥

(2.29)

For a TSA,

(FS)𝑇 =𝑠𝑤𝐵/ cos 𝜃𝑏

𝑃𝑎𝑥 cos 𝜃𝑏 + (𝑊𝑤 + 𝑊𝑠 + 𝑃𝑎𝑧) sin 𝜃𝑏

(2.30)

If θb is 0, then:

(FS)𝑇 =𝑠𝑤𝐵

𝑃𝑎𝑥

(2.31)

The embedment of rigid retaining walls is generally small and passive lateral force is

not taken into account. For gravity retaining structures, with increasing width B of the

wall, the base resistance can be increased. For cantilever walls, the shear key can be

constructed to provide additional base resistance against sliding.

Rotation

A rigid retaining wall must have adequate resistance against rotation. The rotation of the

wall about its toe is satisfied if the resultant vertical force lies within the middle third of

the base. The resultant vertical force at the base is located at

𝑥𝜃 =𝑊𝑤𝑥𝑤 + 𝑊𝑠𝑥𝑠 + 𝑃𝑎𝑧𝑥𝑎 − 𝑃𝑎𝑥𝑧𝑎

(𝑊𝑤 + 𝑊𝑠 + 𝑃𝑎𝑧) cos 𝜃𝑏 − 𝑃𝑎𝑥 sin 𝜃𝑏

(2.32)

Where

𝑧𝑎 is the location of the active lateral earth force from the toe;

If

B/3 ≤ 𝑥 ≤ 2𝐵/3

That is

29

𝑒 = |(𝐵

2− 𝑥)| ≤ 𝐵/6

Where e is the eccentricity of the resultant vertical load, and

𝑥 = 𝑥 cos 𝜃𝑏

If θb is 0, then:

𝑥 =𝑊𝑤𝑥𝑤 + 𝑊𝑠𝑥𝑠 + 𝑃𝑎𝑧𝑥𝑎 − 𝑃𝑎𝑥𝑧𝑎

𝑊𝑤 + 𝑊𝑠 + 𝑃𝑎𝑧

(2.33)

Bearing capacity

A rigid retaining wall must have a sufficient margin of safety against soil bearing

capacity failure. The maximum pressure imposed on the soil at the base of the wall must

not exceed the allowable soil bearing capacity, that is,

(𝜎𝑧)𝑚𝑎𝑥 ≤ 𝑞𝑎 (2.34)

Where

(σz)max is the maximum vertical stress imposed,

qa is the allowable soil bearing capacity.

30

Chapter 3

Laboratory Testing

3.1 Introduction

A series of laboratory tests were conducted in this research, which include liquid limit,

plastic limit, linear shrinkage, X-ray diffraction (XRD) test, shrink-well test, shear box

test and soil-water characteristic curve. In this chapter, the laboratory testing is

discussed in details, which includes set-up and preparation of experiments, soil used for

testing, and the test procedures. The results of tests are presented and discussed as well.

The main objective of this research is to study the swelling pressures of expansive soils.

Swelling in expansive clays is a result of changes in the soil suction or water content.

The swelling pressure can be defined as the pressure required re-compressing, the fully

swollen sample to its original volume.

In this study, oedometer test was used to measure the swelling pressure of expansive

soil. The soils samples used in the laboratory test were collected from the fields at either

Glenroy (a suburb 13 km north of Melbourne), or Braybrook (a suburb 9 km west of

Melbourne).

31

3.2 Atterberg Limit Test

As discussed in Section 2.2.1.1, the Atterberg limits are a basic measure of the nature of

a fine-grained soil. Atterberg Limits Tests consist of Plastic Limit (PL) test and Liquid

Limit (LL) test. In this study, the plastic limit test, liquid limit test and linear shrinkage

test were conducted in accordance with the Australian Standards AS1289. The soil was

firstly dried in an oven at a temperature of 105 oC for two days and was then crushed.

The crushed soil was sieved using a 425μm screen to remove all coarse materials and

vegetable matter (see Figure 3.1)

Figure 3.1: Soil sample preparation

32

3.2.1 Plastic Limit Test

The moisture content at which soil begins to behave as a plastic material is defined as

the plastic limit (PL). PL is determined by rolling out a thread of the soil sample on a

flat and smooth surface. The plastic limit is defined as the moisture content where the

thread just begin to crumble (as shown in Figure 3.2) at a diameter of 3 mm (Budhu

2007). According to AS 1289.3.2.1-2001, the soil sample is rolled by fingers on a glass

plate with rolling rate between 80 to 90 strokes per minutes. A small container that was

weighted before the testing was used to collect the soil thread and to determine the

moisture content.

Figure 3.2: Plastic limit test

The plastic limit wp can be calculated based on AS 1289.3.2.1 (2001):

𝑤𝑝 =𝑚𝑏 − 𝑚𝑐

𝑚𝑐 − 𝑚𝑎

(3.1)

Where

wp = moisture content for plastic limit, in percent

mb = mass of container and wet soil, in grams

mc = mass of container and dry soil, in grams

ma = mass of container, in grams

33

3.2.2 Liquid Limit Test

The liquid limit (LL) is the moisture content at which soil begins to change from the

liquid state to a plastic state. The liquid limit of a soil can be determined by using Four

Point or One Point Casagrande Method. According to AS1289.3.1.2, the Casagrande

cup needs to be checked that the 10 mm calibration gauge will just slide between the

base of the device and the completely raised cup. This gap should be checked each time

before using the device to ensure accuracy of results. It is also important to check that

the grooving tool tip is 2.5mm to ensure the soil sample is closing over a gap of 2.5mm.

Figure 3.3 shows the apparatus used for liquid limit test.

Figure 3.3: Liquid limit test

LL is defined as the moisture content at which two sides of a groove come close

together (Figure 3.3) under the impact of 25 numbers of blows. AS1289.3.1.2 gives the

following equation for determination the liquid limit:

𝑤𝐿 = 𝑤(𝑛

25)𝑡𝑎𝑛𝛽

(3.2)

Where

w = water content;

34

n = number of blows to closure;

tanβ = 0.091.

3.2.3 Linear Shrinkage Test

The shrinkage limit (SL) is the moisture content of a soil at which further loss of

moisture does not result in any more volume reduction.

Test procedures:

Obtain a sample of at least 250 g from the soil passing the 425 µm sieve which has been

prepared in accordance with the procedure prescribed in AS 1289.1 for the preparation

of disturbed soil samples. Alternatively for undisturbed samples, crush the sample using

either or both a mortar and pestle or a machine designed to crush soils to sizes less than

425 µm.

(a) Perform the liquid limit test as described above and ensure a result close to the liquid

limit is achieved.

(b) Lightly grease or oil the inside of a clean shrinkage mold and place the wet soil in it.

Take care to thoroughly remove all air bubbles in the soil by lightly tapping the base of

the mold. Slightly overfill the mold and then level off the excess material with a palette

knife. Remove all soil adhering to the rim of the mold (see Figure 3.4)

(c) Allow the specimen to dry at room temperature for about 24 hours or until a distinct

change in color can be noticed. Transfer into an oven and dry at 105oC, or allow to

continue air-drying, until shrinkage ceases.

(d) Allow the specimen to cool and then measure its longitudinal shrinkage Ls to the

nearest millimeter. If the specimen cracks into pieces, firmly hold the separate parts

together and measure the shrinkage Ls. If the specimen curls (see Figure 3.4), carefully

remove it and measure the length of the top and bottom surfaces. Subtract the mean of

these two lengths from the internal length of the mold to obtain the shrinkage Ls.

35

Figure 3.4: Linear shrinkage test

The shrinkage limit (SL) can be determined by the following equation (from

AS1289.3.4.1, 2008):

SL =𝐿𝑠

𝐿× 100

(3.3)

Where

L= the length of the mold;

Ls = the longitudinal shrinkage of the specimen.

The index properties for Glenroy soil and Braybrook soil are summarised in Table 8.

Based on the Unified Soil Classification System, both Glenroy soil and Braybrook are

classified as clay (Figure 3.5).

Table 8: Results of liquid limit, plastic limit and linear shrinkage tests

Location LL (%) PL (%) PI (%) LS (%)

Glenroy 56.54 16.92 39.61 11.20

Braybrook 80.75 18.02 62.73 22.10

36

Figure 3.5: Plasticity chart showing soil studied

37

3.3 X-ray Diffraction

X-ray diffraction is to study the mineral composition of the soil samples and to

determine percentage crystallinity of samples.

X-ray diffraction analysis was conducted by using a Bruker AXS D4 Endeavour system,

Cu-Kα radiation operated at 40 kV and 40 mA and a Lynxeye linear strip detector. All

samples were in powder form. Microscope slides were used to flatten the surface of all

samples before loading. Samples were tested between 10 and 90 degrees 2 theta with

variable slit v20 with step size 0.02 s.

Figure 3.6: X-ray Diffraction of Glenroy Soil

Figure 3.6 shows the X-ray diffraction result of Glenroy soil. There is 53.1%

crystallinity in the soil. The soil is mainly consists of quartz and muscovite.

Quartz

Muscovite

38

Figure 3.7: X-ray Diffraction of Braybrook Soil

From Figure 3.7, it can be seen that there is 46.9% crystallinity in Braybrook soil, which

is less than that in Glenroy soil. Quartz leads soils to non-expansive. Based on the

results of oedometer test, Braybrook soil can cause larger swelling pressure than

Glenroy soil because of less quartz content in Braybrook soil.

Muscovite

Quartz

39

3.4 The Shrink Swell Test

Australian Standard AS2870 (2011) provides three testing methods for the evaluation of

the reactivity of soil, namely the shrink-swell test (AS1289.7.1.1, 2003), the loaded

shrinkage test (AS1289.7.1.2, 1998) and the core shrinkage test (AS1289.7.1.3, 1998).

The shrink swell test was used for this study because it has two distinct advantages

when compared to the other two methods: (a) both swell and shrinkage strains are

considered so that the sample may be either very wet or very dry; (b) there is no need to

measure soil suction values (Li et al, 2016).

The shrink-swell test, consisting of a core shrinkage test and a swelling test, requires

two identical soil samples which have the same initial moisture content (i.e. one for core

shrinkage test and another for swelling test).

3.4.1 Test Procedure

The core shrinkage test steps are described as follows:

1. An undisturbed cylindrical core sample of a diameter of 45-50 mm was cut

and trimmed to a length within the range of 1.5 to 2 diameters.

2. Initial diameter, length and mass were recorded.

3. Each end of core was placed with a drawing pin that provided a reference

mark for measurements to be taken during the drying procedure.

4. The core was allowed to be air dried on a smooth surface for about two

weeks. Diameter, length and mass were recorded regularly during this period.

5. After about two week drying in the air, the core was oven dried at a

temperature of 105-110 oC for at least 24 hours.

6. After removed out of oven, the length and mass of the core were measured

and final moisture content was determined.

40

Figure 3.8: Core shrinkage test

The total shrinkage strain sh was calculated by the following equation 3.4:

휀𝑠ℎ =100 × (𝐷0 − 𝐷𝑑)

𝐻0

(3.4)

Where

D0 is the distance between the rounded heads of the pins after their placement

(mm)

Dd is the distance between the rounded heads of the pins after removal of

specimen from oven (mm)

H0 is the initial length of the specimen (mm)

41

The apparatus used for the swelling test are shown in Figure 3.9

Figure 3.9: Apparatus used for the swelling test

The swelling test procedure (AS1289.7.1.1, 2003) is as follows:

1. A 50 mm diameter sample was cut with a rigid steel ring of 20mm height

and 45mm in diameter and trimmed carefully to ensure both ends were flat.

The trimmings were collected and used to determine initial moisture content.

2. The specimen was then placed in a consolidation cell with two porous stone

plates at the top and bottom.

3. A seating pressure of 5 kPa was applied for about 10 minutes and the

displacement transducer was zeroed under this seating load to allow for a

small amount of initial settlement of specimen.

42

4. The vertical pressure was then increased to a value equal to the overburden

pressure or 25 kPa (whichever is greater) for a maximum period of 30

minutes. After recording the initial specimen settlement, which was taken as

the datum from which swelling strain was determined, the specimen was

inundated with distilled water and allowed to swell.

5. The swelling displacement of the specimen was regularly monitored during

the swelling procedure.

6. The testing was terminated when the swelling increment was less than 5% of

the total specimen swelling movement for a period of at least of 3 hours.

7. Final moisture content and mass of the specimen was measured at the end of

swelling test.

휀𝑠𝑤 =100 × (𝐷𝑠 − 𝐷𝑖)

𝐻𝑎

(3.5)

Where

Ds = the total swell of the sample after inundation. (mm);

Di = the initial settlement observed prior to inundation (mm);

H0 = the average initial height of the specimen (mm).

43

3.4.2 The Results of shrink swell testing

Knowing the shrinkage strain ss and swelling strain sw, the shrink-swell index, Iss, can

be calculated by the following equation.

𝐼𝑠𝑠 =

휀𝑠𝑤2⁄ + 휀𝑠𝑠

1.8

(3.6)

The calculated shrink-swell index for Glenroy soil is 2.00%/pF while for Braybrook soil

Iss = 4.53%/pF.

44

3.5 Shear Box Tests

In this study, a series of shear box tests was also performed to determine the shear

strength of Glenroy soil. The apparatus used for the testing is shown in Figure 3.10. The

size of the shear box is 60 mm by 60 mm by 20 mm high.

Figure 3.10: Apparatus used for the direct shear testing

The test procedure is as follows

1. Initial moisture content and dry density were determined for each specimen

before the test.

2. The specimen was consolidated in the shear box prior to the shear box testing.

3. Turn on the machine to start the test. During the testing, all readings were taken

by a computer, which include the shear stress, horizontal movement and vertical

movement. The time taken to reach failure (tf) was calculated from the

following equation:

𝑡𝑓 = 50𝑡50 (3.7)

where t50 is the time taken to reach 50% consolidation (minutes)

45

4. The machine stopped and reserved the direction, when the shear box was

reached the limit of travel and the shear box was then bought back to the initial

position.

5. The shear stress versus horizontal displacement curve was plotted. The peak

shear stress was then identified based this curve.

6. Finally a graph of shear stress versus normal stress can be plotted using

Microsoft Excel Spreadsheet.

The relationships between shear stresses and normal stresses for different dry densities

of soil are plotted in Figures 3.11- 3.13. The results of shear box testing on Glenroy soil

are summarised in Table 9.

Figure 3.11: Shear strength vs normal stress (dry density = 14 kN/m3)

46

Figure 3.12: Shear strength vs normal stress (dry density = 17.4 kN/m3)

Figure 3.13: Shear strength vs normal stress (dry density = 18 kN/m3)

47

Table 9: Results of Shear Box Testing

Dry density (kN/m3) c (kPa) (degree) Shear strength

14.0 71.51 49.32 f = 71.51 + tan (49.32o)

17.4 117.67 56.06 f = 117.67 + tan (56.06o)

18.0 292.22 76.94 f = 292.22 + tan (76.94o)

From Table 9, it can be seen that the effective cohesion (c), effective friction angle ()

and shear strength increase with the dry density of soil.

48

3.6 Soil-Water Characteristic Curve

The soil-water characteristic curve (SWCC) also known as the soil-water retention

curve (SWRC) is generally used to present the behavior of deformable unsaturated soil.

It provides the connection between the soil suction and the amount of water in the soil

such as the degrees of saturation. It also gives the essential characteristics of

unsaturated soil. Lots of properties of unsaturated soil such as coefficient of

permeability; shear strength and the amount of water contained in the pores in any

suction can be obtained via the soil-water characteristic curve (Mualem 1976, Fredlund

et al.1994, Wheeler 1996, Assouline 2001).

The air entry value (AEV) is when air begins to go in the greatest pores of the soil. It

can be comprehended as the suction required causing desaturation of the greatest pores,

specified by Fredlund (1996). It can be obtained from SWCC curve as shown in Figure

3.14 which is an example of the soil-water characteristic curve. It is very significant to

know that the desaturation would occur only when the suction is greater than the air

entry value.

Figure 3.14: Expample of soil-water characteristic curve (Sillers et al. 2001)

49

SWCC normally consist of three stages during drying and wetting process:

The Saturation zone, also called capillary saturation zone. The pore water is

tightness and the soil is seeing as fundamentally saturated due to capillary force in

this zone. It continues until the air start to goes in the large pore in the soil sample.

The Desaturation zone: when soil suction value is exceeding the air entry value, the

air will starts to replacing the pore water in the soil, as a result, a significant

decrease appears in the degree of saturation. This zone ends when an increase of

soil suction does not resulting significant changes in the degree of saturation.

The Residual zone, it will be completed due to oven dry conditions where the water

content equals zero, corresponding to a soil suction of approximately 106 kPa

(Croney and Coleman 1961).

A number of the empirical SWCC models/equations have been proposed by different

researchers, which are discussed briefly in the following sections.

Gardner Model (1956)

Gardner proposed an equation which was used for modeling the permeability coefficient

of unsaturated soil in 1956. This equation has been used to model the soil-water

characteristic curve as well.

𝑆𝑟 =1

1 + 𝑎𝜑𝑛

(3.8)

Where Sr is the degree of saturation, is the total suction, a and n are the fitting

parameters.

Brooks and Corey Model (1964)

The very first models used for the soil-water characteristic curve would include the

Brooks and Corey equation.

50

{𝑆𝑟 = 1 𝜑 < 𝑎

𝑆𝑟 = (𝜑

𝑎)−𝑛 𝜑 > 𝑎

(3.9)

The equation specified that SWCC would become an exponentially reducing function

when suction over the air entry value and the SWCC remains constant when suction

value is less than the air entry value.

Van Genuchten Model (1980)

The Van Genuchten model is very popular due to its flexibility and simplicity. Many

researchers have modified this model.

𝑆𝑟 =1

(1 + (𝑎𝜑)𝑛)𝑚

(3.10)

Flexible is a significant advantage of the origin Van Genuchten model, because it

consists three parameters and it is continues model where Brooks and Corey (1961)

does not create the continuous function for the entire SWCC.

Fredlund and Xing Model (1994)

A three parameter continues model for SWCC was created by Fredlund and Xing in

1994:

𝑆𝑟 =1

(ln(𝑒 + (𝑎𝜑)𝑛))𝑚

(3.11)

Where Sr is the degree of saturation, a, n and m are the fitting parameters, e is void ratio

and is soil suction.

This model has great flexibility to fit a wide range of data. Each parameter in the

equation is significant. The achievement of one parameter in the equation could be

distinguished from the effect of the others two parameters, (Sillers and Fredlund, 2001).

51

3.6.1 Testing Procedure

1. The soil sample was collected from Glenroy field site.

2. A cutting ring with an internal diameter of 50 mm was used to cut/trim the soil

sample used for SWCC test.

3. The initial weight and volume of specimen, and the initial soil suction/moisture

content were measured. The initial void ratio of specimen was calculated as well.

4. The specimen was submerged by distill water for approximately two weeks until

it was fully saturated. A small surcharge pressure was applied on the top of the

specimen.

5. After all preparations had been done, sample was placed into the SWCC cell.

6. After a 20 kPa surcharge is applied on the top of the sample, the initial vertical

displacement of specimen and initial water discharged were recorded

7. The water discharged out of the specimen was recorded every day.

8. At the end of test, the specimen was taken out from the sample cell and the final

weight and dimensions of the specimen were measured.

3.6.2 Test Result

The SWCC of Glenroy soil in terms of gravimetric water content and degree of

saturation are plotted in Figure 3.15 and Figure 3.16 respectively. The suction range

above 1500 kPa was obtained by using a Dewpoint Potentiometer (WP4). After SWCC

test, the final mass and volume of the specimen were determined. The specimen was

placed on a smooth surface and left for air dry for three hours. The length and diameter

of the specimen was monitored using a digital vemier caliper. The final suction of the

specimen was measured by the use of WP4 potentiometer. It was assumed that fully dry

soils (i.e., zero water content or zero degree of saturation) had a suction of around

1,000,000 kPa. This value is supported by experimental evidence and theoretical

thermodynamic considerations (Fredlund et al 1994).

52

Figure 3.15: Gravimetric water content versus soil suction for Glenroy soil

53

Figure 3.16: Degree of saturation versus soil suction for Glenroy soil

As can be seen from Figure 3.16 at the beginning of applying matric suction, the soil

specimen has initial gravimetric water content that is 37.87%. A flat reduction is applied

until the suction is increased to 400 kPa, and before 1000 kPa, the moisture content has

decreased rapidly. The suction value above 1500 kPa has been obtained using the WP4

potentiometer test. The shape of the SWCC for Glenroy soil shows flat reduction before

the suction with 400 kPa, which indicates that expansive soil has a high water retention

capability. Composed two plots, the amount of water draining out of the soil during

drying from saturated conditions were accompanied by a corresponding reduction in the

void ratio of the soil.

54

3.7 Oedometer Test

As introduced in Section 2.2.2.1, oedometer testing is one mostly used method to

measure swelling pressure of expansive soils directly. Constant volume method and the

Oedometer test method were studied by Ali and Elturabi (1984). They found that the

oedometer test method might give a slightly higher swelling pressure value than that

obtained from the constant volume method. The oedometer test method was adopted in

this study due to its simplicity. To evaluate the impacts of initial dry density, initial

suction/moisture content on the oedometer swelling test, and three groups of oedometer

tests were performed in this study, in which the samples were prepared at different

initial dry densities and different initial suctions/moisture contents.

3.7.1 Test Procedure

1. After collected from the field site, the soil was firstly dried in an oven at a

temperature of about 105oC and was then crushed.

2. The samples were prepared at different initial suctions/moisture contents

with different initial dry densities

3. The initial soil suction and moisture content of the specimen were measured;

4. The specimen was inundated with distilled water and then a load was applied

on the top of the specimen.

5. Once initial swelling movement decreased, an incremental load was applied

to the specimen;

6. After settlement stop rising up, further loads were applied to the specimen;

7. The above procedure was repeated until the specimen was compressed back

to initial height;

8. The swelling pressure was taken as the pressure that was required to

compress the specimen to its initial height.

55

3.7.2 Results of Oedometer Tests

3.7.2.1 Swelling pressure versus initial suction

Figure 3.17 shows the measured swelling pressures versus the initial soil suctions. The

results show that for both Glenroy and Braybrook soils, the swelling pressure increases

with the initial suction of the soil samples. This is expected because soil suction is a

measure of a soil’s affinity for moisture. As the initial suction increases, for the samples

having the same dry density, the initial degree of saturation will decrease and the

affinity of soil to absorb water will increase. Although there is considerable scatter of

data for Glenroy soil, a reasonably good correlation can be observed between the initial

soil suctions and the measured swelling pressures with R2 of the trend line exceeded 0.8.

Figure 3.17: Swelling pressure versus initial suction

56

3.7.2.2 Swelling pressure versus moisture content

The measured swelling pressure is plotted against the initial moisture contents of soil

samples in Figure 3.18. The swelling pressure of both Glenroy and Braybrook soils

decreases as the initial moisture content increases. This can be attributed to the fact that

at a high water content, the soil is already expanded and has less swelling potential

(Erzin and Erol 2004). From Figure 3.18, it can be seen that the slope of swelling

pressure vs initial moisture content curve of Braybrook soils is much larger than that of

Glenroy soil. This indicates that the impact of the initial moisture content on the

swelling pressure is more significant for highly reactive soil than for low or medium

reactive soil.

Figure 3.18: Swelling pressure versus initial moisture content

57

3.7.2.3 3.7.2.3 Swelling pressure versus dry density

In this group of oedometer tests, the only one variable parameter is the dry density of

expansive soil. Figure 3.19 shows the relationship between the measured swelling

pressure and initial dry density. As expected, the swelling pressure increases with the

initial dry density of soil.

Figure 3.19: Swelling pressure versus dry density

To determine if a correlation exists, the values of the swelling pressure were plotted

against initial dry density in Figure 3.19 using Excel spreadsheet. The equation of the

fitted trend line and R2 values are:

For Glenroy soil Ps = 159.31 d – 2227.3, R2 = 0.9754

For Braybrook soil Ps = 161.48 d – 2048.6, R2 = 0.8674

Where Ps is the swelling pressure and d is the soil dry density.

58

For a correlation to be considered as a reliable mean for estimating the swelling pressure

of a soil, R2 of the trend line needs to exceed 0.8. It is apparent that there is a very good

correlation between Ps and d since the strength of the correlation is 97.54% (i.e. R2 =

0.9754) for Glenroy soil and 86.74% (i.e. R2 = 0.8674) for Braybrook soil. The

laboratory results indicate the dry density is the most important parameter for estimating

the swelling pressure of a soil. Ali and Elturabi (1984) also reported that dry density

gave a more significant indication of swelling pressure than other parameters such as

plastic index. From Figure 3.19, it can be seen that the higher the shrink-swell index (i.e.

Braybrook soil), the larger the predicted swelling pressure.

3.8 Summary

This chapter presents the results of laboratory tests which include the oedometer tests

liquid limit test, plastic limit test, linear shrinkage test, X-ray diffraction (XRD) test,

shrink-swell test, shear box test and soil-water characteristic curve. Based on the shrink-

swell index, liquid limit and plastic limit, Glenroy soil can be classified as a medium

reactive soil while Braybrook soil can be classified as a highly reactive soil. This is

confirmed by X-ray diffraction (XRD) test which indicates that Braybrook soil has a

larger swelling potential than Glenroy soil. The results of the shear box tests indicate

that the shear strength and shear parameters (c and ) increase with the dry density of

the soil. The results of oedometer tests show that the swelling pressure increases with

the initial dry density and initial soil suction but decrease with the soil moisture content.

There is a reasonably good correlation between the swelling pressure and initial soil

suction/moisture content while the correction between the swelling pressure and the soil

dry density is more reliable with the strength of this correlation ranging from 86.74% to

97.54%.

The results of laboratory tests presented in this Chapter provide a good understanding of

the engineering properties of Glenroy soil that was used for the retaining wall

experiments in this study. The retaining wall experiments will be presented in the

following chapter.

59

Chapter 4

Retaining Wall Experiments

4.1 Introduction

Retaining wall has been widely used in civil engineering to support lateral loads from

soils. Currently in Australia, it is generally assumed that the backfill behind a retaining

wall is non-expansive material. However, a retaining wall constructed on expansive soil

may be subjected to significant lateral swelling pressure as a result of soil swelling due

to change in soil moisture. A literature review shows that little research has been carried

out to predict or estimate the horizontal swelling pressure. No direct reference can be

found in the geotechnical literature in Australia and retaining wall model experiments

are almost non-existent.

In order to get better understanding of the lateral swelling pressure developed behind of

a retaining wall, a model retaining wall was built at RMIT Geogechnical Laboratory and

two retaining wall experiments were conducted in this study.

In this chapter, the experimental set-up and procedure are first described, and the testing

results are then presented and discussed.

60

4.2 Soil samples and soil suction measurement

The soil used for laboratory test and retaining wall experiments was obtained from an

expansive soil filed site in Glenroy East, approximately 13 km northern of Melbourne

CBD (Li et al, 2014). After removing vegetation and topsoil, the soil was collected from

a depth of approximately 0.4-0.5 m. After returning to the laboratory, the soil was firstly

dried in an oven at a temperature of about 105oC and then crushed.

The smashed dry soil was mixed at different dry densities and moisture contents, and

used for the oedometer tests to determine the swelling pressure and the retaining wall

model experiments. It was also used for shrink swell test to assess the reactivity of soil

and for shear box tests to obtain shear the strength of soil. All of the laboratory tests

were conducted according to Australian Standards (see Chapter 3).

The initial and final soil suctions were measured using WP4 Potentiometer and the filter

paper method. The Wescor’s in situ soil psychrometers were used to monitor soil

suction changes during retaining wall experiments. Before the lab experiments the soil

psychrometers were calibrated using sodium chloride solutions (Figure 4.1)

Figure 4.1: Psychrometer calibration with Sodium Chloride solutions

61

4.3 Experimental Setup

A model retaining wall apparatus was constructed at RMIT Geotechnical Laboratory to

study the swelling pressure developed behind a retaining wall. Two retaining wall

experiments were conducted in this study. The initial dry density of soil was 17.43

kN/m3 and 14.13kN/m

3 respectively. The dimensions of the model retaining wall are 1

m × 1.4 m × 1 m. Level lines are drawn at 100 mm intervals. The 2 mm thick steel

retaining wall is fixed close to one end of the box, which is structurally supported to

avoid bending of the steel. The resulting size of the void is 1000 × 450 mm in surface

area and 1000 mm deep. A silicon seal was used to prevent any water from leaking

during the test. Five small holes were drilled to fix load cells to the inner side of the

retaining wall. Figure 4.2 shows the arrangement of retaining wall and the locations of

load cells. Five load cells were used to measure lateral loads at different heights:

• Load Cell 1 (H = 100 mm)

• Load Cell 2 and 3 (H = 300 mm)

• Load Cell 4 (H = 500 mm)

• Load Cell 5 (H = 700 mm)

Figure 4.2: Retaining wall arrangement (showing location of load cells)

62

A 50 mm sand layer was placed at the bottom of the void and covered with a layer of

geofabric (960 × 410 mm) in order to prevent mixing of sand and soil. Four timber bars

were placed in the spaces left by the geofabric to further avoid mixing of the different

layers. A 20 mm diameter pipe, 750 mm long was placed into the sand layer running to

the top of the box in order to infiltrate the sand and soil with water. Expansive soil was

then compacted in 50 mm layers. After the first layer was compacted the timber bars

were removed and replaced with Bentonite. As more layers were placed, the load cells

were inserted. Sand was placed around the load cells in order to protect them. Figure 4.3

shows the photos of the set-up.

Figure 4.3: Retaining wall set-up – bottom layer

The filter papers were placed at every two layers (i.e. every 100 mm) from bottom 150

mm. Layers at 150 mm, 250 mm, 350 mm, 450 mm, 550 mm and 650 mm each contain

four pieces of filter paper (24 papers). Larger diameter papers of 70 mm were placed at

63

top and bottom to protect the 47 mm diameter filter paper. The locations of filter papers

are shown in Figure 4.4.

Figure 4.4: Retaining wall arrangement (showing location of filter papers)

Wescor’s in situ soil phychrometer were placed at heights of 200 mm, 450 mm and 650

mm. Another layer of geofabric and timber bars were placed on top of the soil at 750

mm. A final 50 mm sand layer is placed on top of the geofabric. The timber was

removed and again replaced with bentonite. The setup procedure is illustrated in

Figure 4.5.

A concrete block was prepared and placed on the top of the soil to apply a 5 kPa

surcharge. The block had three pipes inserted in it to allow water to readily seep into the

soil. A sixth load cell was placed on top of the concrete block and clamped to the box

with the assistance of a steel beam. This was to restrict the vertical swelling pressure

from the expansive soil, causing all pressure to be lateral pressure. This load cell was

used to measure the vertical swelling pressures. A laser level was placed on top of the

steel beam to measure any vertical movement of the concrete block. Two LVDT devices

placed at the rear of the retaining wall were used to monitor lateral movement of the

wall.

64

Figure 4.5: Retaining wall set up – second layer

Figure 4.6: Retaining wall set up – top concrete block, laser and LVDT devices

65

A data logger was used to take readings from the six load cells, the laser level and the

two LVDT’s every minute. After initial data was taken, 16 liter of water was inserted

through the pipes to infiltrate from top and bottom.

The retaining wall experiment was run for 80 days and results from the data logger are

plotted using Microsoft Excel. The set up schedule of retaining wall experiment 2 was

the same as the first experiment, but there were some differences with the first

experiment. The density of soil was less than that of the first experiment. Only five load

cells were used in the second experiment. There was not a tube at the right hand side of

steel box. Thus the filled water can only seep into soil from the top surface. Figure 4.7

shows the photos of model retaining wall which had been set up and was ready for the

testing.

Figure 4.7: Model retaining wall set up for experiments

66

4.4 Result of Retaining Wall Experiments

Two retaining wall experiments with the same initial moisture content but different

initial dry densities were carried out in this study. The average initial dry density of

Experiment 1 and 2 was 17.43 kN/m3 and 14.13 kN/m

3 respectively The measured

results are presented in the following sections, which include lateral and vertical

swelling pressures, horizontal displacement of retaining wall and suction changes.

4.4.1 The Load Cell Data

Retaining Wall Experiment 1

Figure 4.8 shows the measured total horizontal pressure acting on the wall. As discussed

in Section 4.3, load cell 1 was placed at the center of the retaining wall and 150 mm

from bottom of the wall. For Experiment 1, the water was filled not only from the top

surface but also from bottom side. As can be seen from Figure 4.8, the lateral pressure

measured by load cell 1 increased rapidly at beginning. The pressure reduced slightly

after 8 days and then increased again after 30 days, finally stayed around 40 kPa.

The load cells 2 and 3 were installed at the same height (see Figure 4.2), 200 mm higher

than load cell 1. Load cell 3 was 200 mm left hand side of load cell 2, closer to edge of

the wall. Because of a little gap between the soil and steel wall, water leaked into the

soil from the side of the wall, leading to the lateral pressure measured by load cell 3

which was closer to edge of the wall was much higher than that measured by load cells

1 and 2. From Figure 4.8, it can be seen that lateral swelling pressure recorded by load

cell 3 increased steadily during the first 20 days and then decreased due the fully

saturation of the surrounding soils.

67

Figure 4.8: Measured lateral swelling pressure versus time for load cell 1~3

68

Figure 4.9 shows the data collected from load cell 4 and load cell 5. Load cell 4 was

located in the middle soil layer (Figure 4.2) which was saturated during the last stage of

Experiment 1 since water was added to soil from the top and bottom. From Figure 4.9, it

can be seen that the measured lateral pressure increased sharply after 60 days due to

water seeping into the middle soil layer. The lateral pressure of the top soil layer

(measured by load cell 5) increased steadily from 0 to 80 kPa during the first four days

and then dropped slowly to 20 kPa. It started to increase again after 32 days and reached

to 250 kPa at the end of experiments (Day 81).

Vertical swelling pressure versus time is plotted in Figure 4.10. The vertical swelling

pressure measured by the top load cell increased significantly during the first six days

with a steep slope and then continued to increase until it reached to 500 kPa at day 81.

69

Figure 4.9: Measured lateral swelling pressure versus time for load cell 4 and 5

70

Figure 4.10: Measured vertical swelling pressure versus time

71

Retaining Wall Experiment 2

During retaining wall Experiment 2, water was filled into the soil from the top only.

Figure 4.11 shows the lateral pressure measured by load cells 1-3. The measured lateral

pressure varied with time. During experiment, water seeped into soil through the gap

between soil and the steel wall, leading the soil at the bottom and edge to swell first.

This is why the swelling pressure measured by load cell 1 (at the bottom) and load cell 3

(close to the edge) increased remarkably during the first two days. The soil surrounding

load cell 3 became fully saturated at day 28 and the swelling pressure started to fall

down after 29 days. The swelling pressured measured by load cell 2 increased slowly

and reached to 28 kPa after 82 days. Obviously the soil at the middle of the retailing

wall was not fully saturated at the end of Experiment 2. This is mainly attributed to the

fact that water was only allowed to infiltrate from the top of soil. After the experiment,

the soil samples were taken for soil suction and water content measurements at various

locations. The results show that the soil surrounding load cell 2 was much drier than that

of other locations.

It should be pointed out that only four load cells were used to monitor the lateral

pressure behind of the retaining wall in Experiment 2. As can be seen from Figure 4.12,

the lateral swelling pressure of the top soil (measured by load cell 4) increased

remarkably during the first two days after water was added to soil through three pipes

inserted into the top concrete block. The measured pressure decreased after two day due

to that water infiltrated into the bottom soil layers and increased again at Day 6 when

water was added to the top surface. More water was added at Day 17 and 21, causing

the lateral swelling pressure to reach a peak value of 570 kPa at Day 24.

From Figure 4.13, it can be seen that the vertical swelling pressure increased steadily

with time and reached to a maximum value of 290 kPa at Day 40, which was much

lower than the maximum value of 500 kPa in Experiment 1. This is because that the

initial dry density of the soil used in Experiment 2 was much lower than that used in

Experiment 1.

72

Figure 4.11: Measured lateral swelling pressure versus time for load cells 1, 2 and 3

73

Figure 4.12: Measured swelling pressure versus time for load cell 4

74

Figure 4.13: Measured vertical swelling pressure versus time

75

4.4.2 The Displacement Data

The displacement measurement was used to prove that the wall was not bending. So the

data measured from load cells was the exactly force that could be used.

Retaining Wall Experiment 1

During the model retaining wall experiments, the lateral deformation of the steel wall

was monitored by the use of two LVDT (Linear Variable Differential Transformer)

devices. LVDT 1 was installed at the centre of the retaining wall while LVDT 2 was

located 200 mm below LVDT 1. To restrict the vertical swelling displacement, the top

concrete block was clamped to the steel box with the assistance of a steel beam. The

vertical movement of the concrete block was monitored using a laser device placed on

the top of the steel beam.

Figure 4.14 shows the displacement-time graph for Experiment 1. The measured

displacement generally increased with time. The maximum lateral and vertical

displacements was approximately 0.8 mm and 2 cm respectively.

The displacement versus time for Experiment 2 is plotted in Figure 4.15. While there is

a generally increasing trend in displacements with time, the measured lateral

displacements may be ignored since they are very small. The maximum lateral

displacement was 1.3 mm, slightly larger than that of Experiment 1 while the maximum

vertical displacement of 1.3 mm was lower than that measured in Experiment 1.

76

Figure 4.14: Displacements of retaining wall versus time (Experiment 1)

77

Figure 4.15: Displacements of retaining wall versus time (Experiment 2)

78

4.4.3 Suction Measurement

A retaining wall backfilled with expansive soils may be subjected to a lateral swelling

pressure due to soil suction and volume change. The lateral swelling pressure is

dependent upon soil suction change of the soil media. Therefore the soil suction

measurement is an important part of laboratory experiments.

Soil suction has been introduced in details in Section 2.3, which can be measured

directly or indirectly. Several methods/instruments are valuable for the measurement of

soil suction, which include psychrometers, filter papers, pressure plates, pressure

membranes, tensiometers, and thermal conductivity sensors. Each method has its own

limitations. Tensiometers only work in the low suction range and require frequent

maintenance. Psychrometers are less sensitive in the low suction ranges but sensitive

with the temperature of surrounding environment, and must be calibrated prior to testing.

Pressure membranes, pressure plates and thermal conductivity sensors can only measure

the matric suction. The filter paper method is based on the assumption that a filter paper

will come to equilibrium with soil suction.

In the laboratory, the filter paper method is treated as a reliable test method for measure

of the matric and total suctions of soil sample. Thermal conductivity sensors,

membranes, and pressure plates could only measure the matric suction (Manosuthkij et

al. 2008). Psychrometers need recalibration and maintenance frequently, less sensitive

in low suction range, but sensitive with the temperature of surrounding environment,

and could only measure the total suction. Tensiometers work in low suction range and

daily maintenance is required. The filter paper method of suction measurement is based

on the assumption that a filter paper will come to equilibrium with soil suction. When a

dry filter paper is placed in direct contact with a soil specimen a closed space, there is

direct liquid connectivity between the paper and the soil. It is assumed that equilibrium

is reached by liquid moisture exchange between the soil and the filter paper. Hence, it is

considered that contact filter paper method gives values of matric suction. When a dry

filter paper is suspended above a soil specimen in a closed container, equilibrium is

79

reached by vapor moisture exchange between the soil and the filter paper. The

concentration of this moisture vapour is controlled by the total water potential of the soil

(i.e, total suction).

4.4.3.1 Soil Suction Measured Using Filter Paper Method

The filter paper method was adopted in this study because it is an inexpensive and

relatively simple laboratory test method.

At the end of experiments, the moisture content of the filter papers was determined., the

suction values of the soil were then estimated by using the calibration curve

recommended by ASTM D5298 (2010).

Matric suction

𝑙𝑜𝑔𝜑 = 2.909 − 0.0229𝑤𝑓 , (𝑤𝑓 ≥ 47%) (4.1)

𝑙𝑜𝑔𝜑 = 4.945 − 0.0673𝑤𝑓 , (𝑤𝑓 < 47%) (4.2)

Total suction

𝑙𝑜𝑔𝜑 = 8.778 − 0.222𝑤𝑓 , (𝑤 ≥ 26) (4.3)

𝑙𝑜𝑔𝜑 = 5.31 − 0.0879𝑤𝑓 , (𝑤 < 26) (4.4)

Retaining Wall Experiment 1

The soil suction profiles at the end of Experiment (i.e. after 80 days) are shown in

Figure 4.16. The horizontal locations of filter papers relative to the retaining wall are

also illustrated in Figure 4.16 while the vertical locations of filter papers are shown in

Figure 4.4. The soil suction measured by the filter paper method in this study was

matric suction of the soil, because of filter papers were buried within the soil without

gaps between the soil and papers. As discussed previously, in Experiment 1, water was

80

filled into the soil from both top and bottom. Thus the soil at the top and bottom would

reach a fully saturated state quickly.

From Figure 4.16, it can be seen that the shapes of the soil suction profiles are similar,

i.e. the suction values at the top and bottom were approached to zero while the soil at

the middle had a much higher suction ranging from 2000 kPa to 3300 kPa. In other

words, the retaining wall experiment should have been run longer than 80 days to allow

the maximum lateral swelling pressure to develop behind the retaining wall. However as

the RMIT Civil Engineering Laboratory had to be moved from the City Campus to

Bundoora campus, the retaining wall experiment must be completed within three

months.

Figure 4.16: Matric suction measured using the contact filter paper method

(Experiment 1)

81

It should be noted the soil suction shown in Figure 4.16 is matric suction of the soil

since the contact filter paper method (i.e., the filter papers and soil were in contact) was

used in the lab experiment. In most cases, the water content of the soils can generally be

assumed to correspond to matric suction or total suction when the suctions are greater

than 1500 kPa, i.e., the low suction range up to 1500 kPa represents matric suction and

the high suction range beyond 1500 kPa represents total suction (Li et al 2007).

82

Retaining Wall Experiment 2

In Experiment 2, the water was added to the soil from the top surface only. As shown in

Figure 4.17, the top soil was fully saturated with a very low suction value. The soil

suction increased with the depth. It can be seen that the suction value of the bottom soil

at the right hand side of the retaining wall (the red line) was 322 kPa, much lower than

the suction value of 1740 kPa obtained at the left hand side of the wall (the blue line). A

close inspection revealed that there was a little gap between the wall and soil along the

right hand side corner which allowed water to leak into the soil.

Figure 4.17: Matric suction measured using the contact filter paper method

(Experiment 2)

83

4.4.3.2 Soil Suction Measured Using WP4 Dewpoint Potentiometer

Retaining Wall Experiment 1

After the experiments, the soil samples were collected from the center of soil behind the

retailing wall at the different depths. The soil suctions were measured using a Decagon

WP4-T Dewpoint Potentiometer which uses the chilled-mirror dewpoint technique to

measure total suction. The WP4 was calibrated using a 0.5 Molal/kg solution of

potassium chloride as per the guidelines provided by the manufacturer. The measured

final suction values are plotted in Figure 4.18. It can be seen that the pattern of soil

suction distribution is similar to those plotted in Figure 4.16. The total suction of the top

and bottom of soil was lower because water was filled from both top and bottom of the

soil in Experiment 1. At the end of the experiment (i.e. after 80 days), the water had not

reached to the middle part of the soil.

Figure 4.18: Total suction of the soil behind the center of the wall measured using

WP4 (Experiment 1)

84

Retaining Wall Experiment 2

Figure 4.19 shows the total suction of the soil behind the center of the retailing wall

measured by the use of WP4 at the end of Experiment 2. As discussed previously, in

Experiment 2, the water was filled into the soil from top surface only. Therefore the soil

suction at the top 300 mm was remarkably lower than that of the bottom soil.

Figure 4.19: Total suction of the soil behind the center of the wall measured using

WP4 Experiment 2)

85

4.4.3.3 Soil Suction Measured Using Wescor in situ soil Psychrometer

In the retaining wall experiments, Wescor's in situ soil psychrometers (model PST-55)

were used to monitor the change in soil suction with time during the laboratory

experiments. Three psychrometers were buried within the soil at the different depths

behind the retaining wall. The PST-55 has a stainless steel screen to allow only the

water vapor to enter the sensor.

Retaining Wall Experiment 1

The location of three psychrometers and the measure soil suctions are shown in Figure

4.20 and Figure 4.21 respectively.

Figure 4.20: Location of Psychorometer sensors embedded behind of retaining wall

(Experiment 1)

86

Figure 4.21: Soil suction measured using psychrometers (Experiment 1)

From Figure 4.21, it can be seen that the measured soil suction decreased with time. The

suction value of the bottom soil (red line) and top soil (black line) dropped much

quicker than that of the middle soil (blue line) since water was filled into the soil from

both top and bottom sides. The total soil suctions after 80 days measured by the use of

Wescor's psychrometers (Figure 4.21) agree reasonably well with those obtained by

Decagon WP4-T Dewpoint Potentiometer Figure 4.18.

Retaining Wall Experiment 2

In Experiment 2, three PST-55 psychrometers were installed behind the center line of

the retaining wall as shown in Figure 4.22 .The total soil suctions are plotted versus

time in Figure 4.23. It can be seen that the suction of the top soil (black line) dropped

remarkably during the first week and was maintained at approximately 270 kPa after 20

days. This is because that water was added into the soil from top surface only. The

87

suction of the middle soil (400 mm from the bottom, blue line) decreased gradually with

time as water slowly seeped into the middle soil layer. The suction state of the soil at the

bottom of retaining wall remained almost unchanged.

Figure 4.22: Location of psychorometer sensors embedded behind of retaining wall

(Experiment 2)

88

Figure 4.23: Soil suction measured using psychrometers (Experiment 2)

4.5 Summary

In this study, a model retaining wall was built, and two retaining wall experiments were

carried out to study the horizontal swelling pressure developed behind the retaining wall

due to change in soil moisture. In retaining wall Experiment 1, water was allowed to

seep into the soil from both top and bottom while in Experiment 2, the soil was wetted

from the top surface only. During the experiments, The Wescor's in situ soil

psychrometers were used to monitor the suction variation of the soil behind the

retaining wall. The final suctions of the soil were measured using the contact filter paper

method and Decagon WP4-T Dewpoint Potentiometer.

The results show that the swelling pressure increased with a decrease in soil suction and

an increase in the soil density. The soil suction profiles obtained from WP4

Potentiometer are found to compare very well with those obtained by the use of the

filter paper method. The soil suctions measured by Wescor's psychrometers agree

89

reasonably well with those measured by using WP4 Potentiometer and the filter paper

method.

Due to the lab relocation, the retaining wall experiments had to be completed after 80

days. The measured final soil suction values clearly show that 80 days are not long

enough for the soil behind the retaining wall to reach a full saturation state.

90

Chapter 5

Development of New Model for Prediction of Lateral Swelling Pressure

5.1 Introduction

Based on the laboratory tests, an empirical equation is proposed for predicting the

lateral swelling pressure of a retaining wall. Three parameters, namely the initial dry

density, initial moisture content and soil shrink-swell index are taken into account. The

constants adopted in the proposed empirical equation are obtained through multiple

regression analysis (MRA). Although a few empirical equations for the prediction of

horizontal swelling pressure are available in literature internationally, no research has

been done in Australia. Therefore there is a need to develop a new method/model for

local engineers so the lateral swelling pressure can be estimated based on the soil

indices widely used in the routine practice in Australia.

There are several empirical equations available for prediction of swelling pressure.

Erzin and Erol (2007) carried out multiple regression analysis based on the results of

experiments on statically compacted samples of Bentonite-Kaolinite clay mixtures.

They found that following equations have strong correlations between the swelling

pressure and the soil properties.

𝐹𝑜𝑟 0 < 𝑃𝑠 ≤ 100 𝑘𝑃𝑎;

𝑃𝑠 = −3.72 + 0.0111𝑃𝐼 + 2.077𝛾𝑑 + 0.244 log 𝑠 R=0.96 (5.1)

𝐹𝑜𝑟 100 < 𝑃𝑠 ≤ 350 𝑘𝑃𝑎;

𝑃𝑠 = −16.31 + 0.0330𝑃𝐼 + 8.253𝛾𝑑 + 0.829 log 𝑠 R=0.97 (5.2)

Where

𝑃𝑠 = 𝑆𝑤𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑘𝑔/𝑐𝑚2);

𝑃𝐼 = 𝑃𝑙𝑎𝑠𝑡𝑖𝑐 𝑖𝑛𝑑𝑒𝑥 (%);

𝛾𝑑 = 𝐷𝑟𝑦 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (𝑔/𝑐𝑚3);

𝑠 = 𝑠𝑜𝑖𝑙 𝑠𝑢𝑐𝑡𝑖𝑜𝑛 (𝑏𝑎𝑟).

91

Elisha (2012) performed one-dimensional swell tests on soil samples specimens with

variable properties in oedometers. The relationship between swelling pressure and

plasticity index (PI), water content (w) and dry density (d) were examined. The

multiple regression analysis was used to develop the following equation to estimate the

logarithm of the swelling pressure:

log 𝑃𝑠 = −5.423 + 0.01458𝑃𝐼 + 2.563𝛾𝑑 − 0.0168𝑤 R2 = 0.95 (5.3)

5.2 The proposed new model

In this study, a new model/equation relating swelling pressure, in terms of shrink-swell

index, initial dry density and initial moisture content, was proposed:

log 𝑃𝑠 = 𝑎 + 𝑏 𝐼𝑠𝑠 + 𝑐𝛾𝑑 + 𝑑𝑤𝑖 (5.4)

Where

𝑃𝑠 = 𝑆𝑤𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑘𝑃𝑎);

𝑤𝑖 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 (%);

𝛾𝑑 = 𝐷𝑟𝑦 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (𝑘𝑁/𝑚3);

𝐼𝑠𝑠 = 𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑎𝑛𝑑 𝑠𝑤𝑒𝑙𝑙 𝑖𝑛𝑑𝑒𝑥 (%/𝑝𝐹);

𝑎, 𝑏, 𝑐, 𝑑 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑠;

The multiple regression analysis was carried out using Metlab to obtain the fitting

parameters a, b, c and d (see Figure 5.1 and Figure 5.2):

log 𝑃𝑠 = −0.2849 + 0.0686𝐼𝑠𝑠 + 0.1851𝛾𝑑 − 0.0318𝑤𝑖 R2

= 0.94 (5.5)

The result shows that the logarithm swelling pressure has strong correlations with soil

properties that consist of shrink swell index, initial dry density and initial moisture

content as the strength of this correlation is 94% (i.e. R2 = 0.94).

92

Figure 5.1: Multiple regression analysis by Metlab

93

Figure 5.2: Regression equation obtained using Metlab

94

Figure 5.3 shows the effect of initial dry density on the swelling pressure for the

proposed method. The swelling pressure increases with increasing initial dry density for

the soils having the same initial moisture content and shrink-swell index. An increase in

soil dry density leads to smaller volume for water particles to move. During water

absorption, water particles can exert greater force to the surrounding soil particles to

achieve the complete saturation. Consequently the soil swelling pressure will be higher

as results of these increased inter-particle forces.

Figure 5.3: Effect of initial dry density on the predicted swelling pressure

95

Figure 5.4 shows the relationship between the swelling pressure predicted by the proposed

equation and the initial moisture content for Glenroy soil having the same initial dry density.

The swelling pressure decreases as the initial moisture content increases.

Figure 5.4: Effect of initial moisture content on the predicted swelling pressure

Figure 5.5 shows the effect of shrink-swell index (Iss) on the swelling pressure for the

proposed method. It can be seen that for the soils having the same initial dry density and

initial moisture content, the predicted swelling pressure increases with the shrink-swell index.

96

Figure 5.5: Effect of shrink-swell index on the predicted swelling pressure,

5.3 Summary

A new model/equation has been proposed for prediction of the lateral swelling pressure using

the initial dry density, initial water content and shrink and swell index. The main advantage

of this new model is its simplicity as all parameters can be obtained by conventional

laboratory geotechnical tests.

97

Chapter 6

Conclusions and Recommendations

6.1 Conclusions

In this study, a model retaining wall was built, and two retaining wall experiments were

carried out to evaluate the lateral swelling pressure developed behind the retaining wall due

to change in soil moisture content (suction). Fifteen groups of oedometer swelling tests were

performed on samples with different initial moisture contents/soil suction values and different

initial dry densities. In addition to retaining wall model tests and constant volume swell tests,

a series of other laboratory tests were also performed, including liquid limit test, plastic limit

test, linear shrinkage test, X-ray diffraction (XRD) test, soil-water characteristic curve, shear

box test, shrink-swell test, and soil suction measurement.

The following conclusions can be drawn from the testing results:

Swelling pressure developed within soil depends on the initial moisture content of the

soil mass. Swelling pressure decreases with an increase of initial moisture content for

the soil having the same initial dry density.

Both the model retaining wall experiments and constant volume swell tests show that

swelling pressure increases with the initial dry density for the soil having the same

initial moisture content.

Swelling pressure increases with the initial soil suction for the soil having the same

initial dry density.

Swelling pressure increases as the shrink-swell index Iss increases.

Based on the laboratory tests, an empirical equation has been developed for estimating the

lateral swelling pressure of unsaturated expansive soils behind of retaining walls. This

equation can be used for prediction of horizontal swelling pressure based on initial moisture

content, initial dry density and the shrink-swell index which is widely used in Australia for

classification of expansive soil sites.

98

6.2 Recommendations for Further Work

It is recommended that further research be carried out in the following areas:

1. Due to laboratory relocation, only two retaining wall experiments were carried out and

each experiment was run for 80 days. The results clearly indicate that at the end of the

experiments, the soil behind the retaining wall had not been fully saturated yet. More

retaining wall experiments are required to further evaluate the lateral swelling

pressure developed behind the wall as a result of a change in soil moisture content

(suction). The experiments should be allowed to run more than six months if possible.

2. Due to time limitation, only fifteen groups of oedometer swelling tests were

performed on two types of soil. More tests are required for different soils with various

initial dry densities, various initial moisture contents (suction values) and different

shrink-swell indices.

3. Further study of the effect of initial dry density, initial moisture content (suction) and

shrink-swell index on the swelling pressure is also needed.

99

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